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Solskjaer managed the Norwegian side back in 2015 and they took on Ajax in the Europa League, who had a young van de Beek in midfield.
He scored in the 1-1 draw and Solskjaer told BBC's Football Daily the Dutchman left a lasting impression, for a number of reasons.
"The first goal he scored was against me and my Molde team in the Europa League in 2015 - we drew 1-1 at the Amsterdam Arena and he scored a fantastic header," the 47-year-old begun.
"He actually headbutted my centre-back at the time as well, so he was brave! I've liked his infectious attitude. I've spoken to Edwin van der Sar, other players that know him, you just use the people you know and trust to scout that character.
"When someone scores against you, you'll always remember it...I just remember a cross and he beats my centre-back and it loops over our keeper in the beginning of the game."
Van de Beek became United's first summer signing last week and when asked what he'll bring to Old Trafford, Solskjaer replied: "When we signed Bruno [Fernandes] we knew we needed that kind of player, now we've signed Donny and he's a type of player I felt we needed in the squad.
Some men just look born to play for United.- Manchester United (@ManUtd) September 9, 2020
We think we've found one. pic.twitter.com/W8QkwBX2Jn
"He's the type of person that will fit the culture, fit the team and improve us next season and for years to come.
"He's a versatile player, a very intelligent player, he's got loads of energy, enthusiasm, developing all the time. He scores goals and we need to add those from midfield. We need goals throughout the squad because we didn't score enough [last season] to be challenging at the top.
"He can see space and arrive at the right time, the timing of his movements is fantastic."
The 23-year-old netted 10 goals in all competitions last season and will add strong depth to the Red Devils midfield.
Do you think Donny van de Beek will be a good signing for Manchester United?
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Featured Image Credit: PA Images & Manchester United
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